In physics, a harmonic oscillator is a system that undergoes repetitive, or oscillatory, motion around a fixed point or equilibrium position. This motion is characterized by a specific frequency, or rate of oscillation, which depends on the properties of the system.

A common example of a harmonic oscillator is a mass attached to a spring. When the mass is displaced from its equilibrium position and then released, it begins to oscillate back and forth around the equilibrium position. The frequency of the oscillation is determined by the mass of the object, the spring constant of the spring, and the amplitude of the oscillation.

Another example of a harmonic oscillator is a pendulum. A pendulum consists of a mass attached to a rigid rod or string that is suspended from a fixed point. When the mass is displaced from its equilibrium position and then released, it begins to swing back and forth around the equilibrium position. The frequency of the oscillation is determined by the length of the pendulum and the acceleration due to gravity.

Harmonic oscillators are important in physics because they can be used to model many different types of systems, from simple mechanical systems like springs and pendulums to more complex systems like atoms and molecules. They also have many practical applications, such as in the design of oscillators for electronic circuits, in the study of waves and vibrations in materials, and in the development of instruments for measuring small forces and displacements.